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Exam 20: Transportation Models

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Question 21

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Which of the following is not needed in order to use the transportation model?

A) the source points and their capacity
B) the fixed costs of source points
C) the destination points and their demand
D) the cost of shipping one unit from each source to each destination
E) All of these are needed.

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Question 22

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The transportation model seeks satisfactory, but not necessarily optimal, solutions for shipping goods from several origins to several destinations.

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Question 23

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Source A has capacity of 15, Source B has capacity of 30, Destination 1 has demand of 5 and Destination 2 has demand of 20. Fill in the following table with the correct initial solution for a Northwest-corner method approach. $\begin{array} { | l | c | c | c | } \hline & \text { Destination 1 } & \text { Destination 2 } & \text { Dummy Destination } \\\hline \text { Source A } & 5 & 10 & \\\hline \text { Source B } & & 10 & 20 \\\hline\end{array}$

The three information needs of a transportation problem are the origin points and the capacity at each, the destination points and the demand at each, and ________.

In a minimization problem, a negative improvement index in a cell indicates that the

Find the minimum cost solution for the transportation problem detailed in the table below. Explain carefully the meaning of any quantity in a "dummy" row or column. $\begin{array} { | l | r | r | r | r | } \hline \text { COSTS } & \text { Dest 1 } & \text { Dest 2 } & \text { Dest 3 } & \text { Supply } \\\hline \text { Source 1 }& 30 & 12 & 5 & 20 \\\hline \text { Source 2 }& 10 & 14 & 12 & 30 \\\hline \text { Source 3 }& 20 & 11 & 25 & 75 \\\hline \text { Dummy } & 0 & 0 & 0 & 30 \\\hline \text { Demand }& 40 & 60 & 55 & 155 \backslash 155 \\\hline \end{array}$

The Shamrock Transportation Company has four terminals: A, B, C, and D. At the start of a particular day, there are 8, 8, 6, and 3 tractors available at those terminals, respectively. During the previous night, trailers were loaded at plants R, S, T, and U. The number of trailers at each plant is 2, 12, 5, and 6, respectively. The company dispatcher has determined the distances between each terminal and each plant, as follows. How many tractors should be dispatched from each terminal to each plant in order to minimize the total number of miles traveled? $\begin{array} { | l |r | r | r | r | r | } \hline \text { COSTS } & { \text { Dest. 1 } } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \\\hline \text { Origin 1 } & 21 & 44 & 25 & 40 & 8 \\\hline \text { Origin 2 } & 42 & 24 & 45 & 22 & 8 \\\hline \text { Origin 3 } & 78 & 32 & 42 & 55 & 6 \\\hline \text { Origin 4 } & 44 & 42 & 32 & 30 & 3 \\\hline \text { Demand } & 2 & 12 & 5 & 6&25/25 \\\hline\end{array}$

The number of routes filled by a solution to a transportation problem is no larger than ________.

The transportation method is a special case of the family of problems known as

Degeneracy in a transportation problem is when no closed path exists for evaluating an unused cell.

In formulating a transportation problem, you discover that one of the route combinations is forbidden by contract, or prohibited by law, or ruled out by company policy. How would you indicate the cost of that cell in preparing the problem to be solved?

Consider the transportation problem in the data set and optimal solution below. Calculate improvement indices on each empty cell. Is this solution optimal? $\begin{array}{|l|r|r|r|r|r|}\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \\\hline \text { Source 1 } & 12 & 18 & 9 & 11 & 105 \\\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \\\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \\\hline \text { Demand } & 80 & 60 & 70 & 90 & 300/300 \\\hline\end{array}$ $\begin{array}{|lrrrrr|}\hline \text { Shipments } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Row Total } \\\text { Source 1 } & 30 & 0 & 70 & 5 & 105 \\\text { Source 2 } & 0 & 60 & 0 & 85 & 145 \\\text { Source 3 } & 50 & 0 & 0 & 0 & 50 \\\text { Col. Total } & 80 & 60 & 70 & 90 & 300 \backslash 300 \\\hline\end{array}$

A transportation problem has 11 origins and 16 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

The purpose of the transportation approach for location analysis is to minimize

A transportation problem has 20 origins and 32 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

The stepping-stone method

Which of the following combinations of sources and destinations would fill no more than 25% of cells with quantities to be shipped for the optimal solution?

A transportation problem has 6 origins and 12 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

The stepping-stone method frequently achieves an optimal solution as soon as it calculates an initial feasible solution.

Source A has capacity of 25, Source B has capacity of 35, Destination 1 has demand of 15 and Destination 2 has demand of 20. Fill in the following table with the correct initial solution for a Northwest-corner method approach. $\begin{array} { | c | c | c | c | } \hline & \text { Destination 1 } & \text { Destination 2 } & \text { Dummy Destination } \\\hline \text { Source A } & 15 & 10 & \\\hline \text { Source B } & & 10 & 25 \\\hline\end{array}$